Related papers: A Tenth Hilbert Problem-like Result: The Decidabil…
The use of finite entanglement scaling with matrix product states (MPS) has become a crucial tool for studying 1+1d critical lattice theories, especially those with emergent conformal symmetry. We argue that finite entanglement introduces a…
Some new decidability results for multiplicative matrix equations over algebraic number fields are established. In particular, special instances of the so-called knapsack problem are considered. The proofs are based on effective methods for…
In this paper, the known deterministic linear-quadratic Stackelberg game is revisited, whose open-loop Stackelberg solution actually possesses the nature of time inconsistency. To handle this time inconsistency, {a two-tier game framework…
We prove that the pattern matching problem is undecidable in polymorphic lambda-calculi (as Girard's system F) and calculi supporting inductive types (as G{\"o}del's system T) by reducing Hilbert's tenth problem to it. More generally…
One of the main open problems in the context of extensions of Hilbert's tenth problem (HTP) is the case of the ring of complex entire functions in one variable. Our main result provides a step towards an answer: For every $\rho\ge 0$, we…
The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a "bad variable" construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
The aim of this paper is two-fold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and secondly, we discuss the existence of…
Machine Learning explainability techniques have been proposed as a means of `explaining' or interrogating a model in order to understand why a particular decision or prediction has been made. Such an ability is especially important at a…
This paper investigates a series of optimization problems for one-counter Markov decision processes (MDPs) and integer-weighted MDPs with finite state space. Specifically, it considers problems addressing termination probabilities and…
Previous work has shown that reasoning with real-time temporal logics is often simpler when restricted to models with bounded variability---where no more than v events may occur every V time units, for given v, V. When reasoning about…
Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem…
The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product {\it ansatz}. Due to the similarity of the master equation and the Schr\"odinger equation at imaginary times the…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with…
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $\xi_t\in V_t$, admitting an equivalent martingale measure. The aim of this…
We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the…
This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…